The angular momentum transport by standard MRI in quasi-Kepler cylindrical Taylor-Couette flows

Gellert, M.; Rüdiger, G.; Schultz, M.

doi:10.1051/0004-6361/201117892

Cited by 9 publications

(9 citation statements)

References 20 publications

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“…For small magnetic Prandtl numbers (here Pm = 0.01) we again find a crossing phenomenon for strong fields in the neutral-stability curves for m = 0 and m = 1 [60]. In Fig.…”

Section: Quasi-keplerian Flowsupporting

confidence: 65%

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Stability and instability of hydromagnetic Taylor–Couette flows

et al. 2018

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Decades ago S. Lundquist, S. Chandrasekhar, P. H. Roberts and R. J. Tayler first posed questions about the stability of Taylor-Couette flows of conducting material under the influence of large-scale magnetic fields. These and many new questions can now be answered numerically where the nonlinear simulations even provide the instability-induced values of several transport coefficients. The cylindrical containers are axially unbounded and penetrated by magnetic background fields with axial and/or azimuthal components. The influence of the magnetic Prandtl number Pm on the onset of the instabilities is shown to be substantial. The potential flow subject to axial fields becomes unstable against axisymmetric perturbations for a certain supercritical value of the averaged Reynolds number Rm = √Re · Rm (with Re the Reynolds number of rotation, Rm its magnetic Reynolds number). Rotation profiles as flat as the quasi-Keplerian rotation law scale similarly but only for Pm 1 while for Pm 1 the instability instead sets in for supercritical Rm at an optimal value of the magnetic field. Among the considered instabilities of azimuthal fields, those of the Chandrasekhar-type, where the background field and the background flow have identical radial profiles, are particularly interesting. They are unstable against nonaxisymmetric perturbations if at least one of the diffusivities is non-zero. For Pm 1 the onset of the instability scales with Re while it scales with Rm for Pm 1. Even superrotation can be destabilized by azimuthal and current-free magnetic fields; this recently discovered nonaxisymmetric instability is of a double-diffusive character, thus excluding Pm = 1. It scales with Re for Pm → 0 and with Rm for Pm → ∞.The presented results allow the construction of several new experiments with liquid metals as the conducting fluid. Some of them are described here and their results will be discussed together with relevant diversifications of the magnetic instability theory including nonlinear numerical studies of the kinetic and magnetic energies, the azimuthal spectra and the influence of the Hall effect.

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“…For small magnetic Prandtl numbers (here Pm = 0.01) we again find a crossing phenomenon for strong fields in the neutral-stability curves for m = 0 and m = 1 [60]. In Fig.…”

Section: Quasi-keplerian Flowsupporting

confidence: 65%

“…The wave numbers in Fig. 42 must be interpreted using (60) so that for kR 0 3π (horizontal dotted line) the cells are almost circular in the (R/z) plane. Below the horizontal dotted line the cells are all oblong with respect to the rotation axis.…”

Section: Influence Of Boundary Conditionsmentioning

confidence: 99%

Stability and instability of hydromagnetic Taylor–Couette flows

et al. 2018

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“…By appropriately choosing the rotation ratio of the cylinders, velocity profiles of the general form w( ) r r q , including = -q 1.5 for Keplerian rotation, can be well approximated experimentally at very large Reynolds numbers (Edlund & Ji 2015;Lopez & Avila 2017). For an imposed axial magnetic field, Gellert et al (2012) found the transport coefficient α to be independent of magnetic Reynolds Rm and magnetic Prandtl Pm numbers, only scaling linearly with the Lundquist number S of the axial magnetic field. (Nornberg et al 2010), unstable magnetocoriolis waves (giving rise to the MRI) have not been reported in the literature so far.…”

Section: Introductionmentioning

confidence: 97%

Transport Properties of the Azimuthal Magnetorotational Instability

Guseva

Willis

Hollerbach

et al. 2017

ApJ

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The magnetorotational instability (MRI) is thought to be a powerful source of turbulence in Keplerian accretion disks. Motivated by recent laboratory experiments, we study the MRI driven by an azimuthal magnetic field in an electrically conducting fluid sheared between two concentric rotating cylinders. By adjusting the rotation rates of the cylinders, we approximate angular velocity profiles w µ r q . We perform direct numerical simulations of a steep profile close to the Rayleigh line  -q 2 and a quasi-Keplerian profile » -q 3 2 and cover wide ranges of Reynolds ( Ŕe 4 10 4 ) and magnetic Prandtl numbers (   0 Pm 1). In the quasi-Keplerian case, the onset of instability depends on the magnetic Reynolds number, with » Rm 50 c , and angular momentum transport scales as Pm Re 2 in the turbulent regime. The ratio of Maxwell to Reynolds stresses is set by Rm. At the onset of instability both stresses have similar magnitude, whereas the Reynolds stress vanishes or becomes even negative as Rm increases. For the profile close to the Rayleigh line, the instability shares these properties as long as 

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“…Rotation excites the instability, but it can also be too fast for its existence. This is quite opposite to the excitation conditions of the axisymmetric (or channel) modes of standard MRI (Gellert et al 2012) or HMRI with negative shear (Stefani et al 2006;Rüdiger et al 2018a) which do not possess upper limits of the Reynolds number. The HMRI with super-rotation is thus much more stable than HMRI with sub-rotation.…”

Section: The Axisymmetric Modes In Their Dependence On the Magnetic Prandtl Numbermentioning

confidence: 58%

“…The stability maps for non-axisymmetric modes of a fluid rotating beyond the Rayleigh limit (e.g. quasi-Keplerian rotation) show for any given Lundquist number of the axial magnetic field a lower critical Reynolds number for the MRI onset and a maximal one where the diffusion stops the instability (Gellert, Rüdiger & Schultz 2012). The minimum rotation rates of the lines of neutral stability scale with Pm Re const for small Pm, and with √ Pm Re const.…”

Section: Introductionmentioning

confidence: 98%

Destabilization of super-rotating Taylor–Couette flows by current-free helical magnetic fields

2021

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In an earlier paper we showed that the combination of azimuthal magnetic fields and super-rotation in Taylor–Couette flows of conducting fluids can be unstable against non-axisymmetric perturbations if the magnetic Prandtl number of the fluid is $\textrm {Pm}\neq 1$ . Here we demonstrate that the addition of a weak axial field component allows axisymmetric perturbation patterns for $\textrm {Pm}$ of order unity depending on the boundary conditions. The axisymmetric modes only occur for magnetic Mach numbers (of the azimuthal field) of order unity, while higher values are necessary for the non-axisymmetric modes. The typical growth time of the instability and the characteristic time scale of the axial migration of the axisymmetric mode are long compared with the rotation period, but short compared with the magnetic diffusion time. The modes travel in the positive or negative $z$ direction along the rotation axis depending on the sign of $B_\phi B_z$ . We also demonstrate that the azimuthal components of flow and field perturbations travel in phase if $|B_\phi |\gg |B_z|$ , independent of the form of the rotation law. Within a short-wave approximation for thin gaps it is also shown (in an appendix) that for ideal fluids the considered helical magnetorotational instability only exists for rotation laws with negative shear.

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The angular momentum transport by standard MRI in quasi-Kepler cylindrical Taylor-Couette flows

Cited by 9 publications

References 20 publications

Stability and instability of hydromagnetic Taylor–Couette flows

Stability and instability of hydromagnetic Taylor–Couette flows

Transport Properties of the Azimuthal Magnetorotational Instability

Destabilization of super-rotating Taylor–Couette flows by current-free helical magnetic fields

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